I finally figured it out on my own. Here is the solution in case anyone else runs into this.
Blur an image...
$imagick = new Imagick($image);
$imagick->blurImage(0,$blur_radius);
$imagick->writeImage($output_image);
Add an overlay to an image...
$imagick = new Imagick($image);
$overlay = new Imagick($filter_image);
$imagick->compositeImage($overlay, imagick::COMPOSITE_SOFTLIGHT, 0, 0);
$imagick->writeImage($output_image);
You can easily combine the two methods as well and blur the image and then add a composite overlay to it.
$imagick = new Imagick($image);
$imagick->blurImage(0,$blur_radius);
$overlay = new Imagick($filter_image);
$imagick->compositeImage($overlay, imagick::COMPOSITE_SOFTLIGHT, 0, 0);
$imagick->writeImage($output_image);